... where U0 and a are positive constants. It has a total mechanical energy −U0 < E < 0.
Sketch the potential energy as a function of x and show (analytically) that x = 0 is a point
of stable equilibrium. Find the “classical turning points” xm , that is the maximum and
minimum values of x, in terms of E ...
... Dynamics, Newton’s Laws (Summary)
• Dynamics deals with why objects move as they do
• The Concept of FORCE
• Forces are Vectors
• Contact Forces: push, pull
• Forces at a distance: gravity, electromagetic
• The NET FORCE on a body is the vector sum
of all forces acting on the body
... Wave packets; phase and group velocities; de Broglie waves; energy density and intensity.
Lorentz transformation matrix; space and time four vectors; force and energy in relativistic mechanics
The Lagrangian and Hamiltonian
Generalized coordinates; Lagrangian formulation and appli ...
... If body A exerts a force F AB (action) on body B, then body B
exerts a force FBA (reaction) on A of the same intensity but in
the opposite direction. In other words, for every action there is an
equal and opposite reaction:
FAB = - F BA
The forces of action and reaction act on different bodies.
... change in the motion of an object
Acceleration – change of velocity or
Velocity – the rate of speed with which
Speed – rate of motion
Friction – the resistance of movement on
surfaces that touch.
Mass – the amount of matter in an object
... 11. An electron moving with an intital velocity enters an electric field E(t)ˆ1
with a velocity V0 ˆ1 . The acceleration is given by ~a = eE(t)ˆ1 /m, where m
is the mass of the electron. The magnitude of the electric field is given by
E(t) = 0 for t < 0 ; E(t) =